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Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation

Author

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  • Yumiao Tian

    (Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China)

  • Maorong Ge

    (Institute of Geodesy and Geoinformation Science, Technische Universität Berlin, 10623 Berlin, Germany
    Section 1.1: Space Geodetic Techniques, GFZ German Research Centre for Geosciences, 14473 Potsdam, Germany)

  • Frank Neitzel

    (Institute of Geodesy and Geoinformation Science, Technische Universität Berlin, 10623 Berlin, Germany)

Abstract

Global navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of GNSS phase bias estimation encounters the rank-deficiency problem, making bias estimation a difficult task. Combining the Monte-Carlo-based methods and GNSS data processing procedure can overcome the problem and provide fast-converging bias estimates. The variance reduction of the estimation algorithm has the potential to improve the accuracy of the estimates and is meaningful for precise and efficient PNT services. In this paper, firstly, we present the difficulty in phase bias estimation and introduce the sequential quasi-Monte Carlo (SQMC) method, then develop the SQMC-based GNSS phase bias estimation algorithm, and investigate the effects of the low-discrepancy sequence on variance reduction. Experiments with practical data show that the low-discrepancy sequence in the algorithm can significantly reduce the standard deviation of the estimates and shorten the convergence time of the filtering.

Suggested Citation

  • Yumiao Tian & Maorong Ge & Frank Neitzel, 2020. "Variance Reduction of Sequential Monte Carlo Approach for GNSS Phase Bias Estimation," Mathematics, MDPI, vol. 8(4), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:522-:d:341014
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    References listed on IDEAS

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    1. Tuffin Bruno, 1996. "On the use of low discrepancy sequences in Monte Carlo methods," Monte Carlo Methods and Applications, De Gruyter, vol. 2(4), pages 295-320, December.
    2. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(5), pages 933-956, October.
    3. Pierre L’Ecuyer & Christiane Lemieux, 2002. "Recent Advances in Randomized Quasi-Monte Carlo Methods," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 419-474, Springer.
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    Cited by:

    1. Dong-Kyeong Lee & Yebin Lee & Byungwoon Park, 2023. "Carrier Phase Residual Modeling and Fault Monitoring Using Short-Baseline Double Difference and Machine Learning," Mathematics, MDPI, vol. 11(12), pages 1-21, June.

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